(X-4)(480/x+3)=480

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Solution for (X-4)(480/x+3)=480 equation: 



(X-4)(480/X+3)=480

We move all terms to the left:

(X-4)(480/X+3)-(480)=0



Domain of the equation: X+3)!=0

X∈R



We multiply parentheses ..

(+480X^2+3X-1920X-12)-480=0

We get rid of parentheses

480X^2+3X-1920X-12-480=0

We add all the numbers together, and all the variables

480X^2-1917X-492=0

a = 480; b = -1917; c = -492;
Δ = b2-4ac
Δ = -19172-4·480·(-492)
Δ = 4619529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:


$\sqrt{\Delta}=\sqrt{4619529}=\sqrt{9*513281}=\sqrt{9}*\sqrt{513281}=3\sqrt{513281}$


$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1917)-3\sqrt{513281}}{2*480}=\frac{1917-3\sqrt{513281}}{960}
$


$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1917)+3\sqrt{513281}}{2*480}=\frac{1917+3\sqrt{513281}}{960}
$

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